This article is concerned with incipient plasticity in an InP crystal studied by nanoindentation experiments and ab initio simulations. We consider dislocation-nucleation phenomena and pressure-induced phase transformation to be the alternative mechanisms that govern the elastic-plastic transition displayed by the InP crystal. The ab initio calculations have shown that S-and Zn-doping of the low-pressure zinc blende structure of InP decreases the pressure of phase transformation of the rock-salt structure. The nanoindentation examination of undoped as well as S-and Zn-doped crystals of (001) and (111) orientation revealed an increase in contact pressure at the onset of plastic behavior (pop-in) for doped specimens. As they are contrary to the outcomes of the ab initio simulations, the results of nanoindentation experiments point toward dislocation nucleation as an origin of InP incipient plasticity. Additional investigations were performed on an undoped as well as Si-doped GaAs crystal, which showed that the contact pressure at the pop-in event takes a lower value for the Si-doped sample than the undoped sample. This result is in contrast to the case of the InP crystal displaying phase transformation-steered incipient plasticity of GaAs. Our investigations exhibit the complexity of the semiconductor's nanodeformation simultaneously providing a convenient way to identify its incipient plasticity mechanism.